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The value of sin(pi/18)+sin(pi/9)+sin((2...

The value of `sin(pi/18)+sin(pi/9)+sin((2pi)/9)+sin((5pi)/18)` is

A

`sin""(7pi)/(18)+sin""(4pi)/(9)`

B

1

C

`cos""(pi)/(6)+cos""(3pi)/(7)`

D

`cos""(pi)/(9)+sin""(pi)/(9)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given expression, `sin""(pi)/(18)+sin""(pi)/(9)+sin""(2pi)/(9)+sin""(5pi)/(18)`
`" "=sin10^(@)+sin20^(@)+sin40^(@)+sin50^(@)`
`" "=sin50^(@)+sin10^(@)+sin40^(@)+sin20^(@)`
`" "=sin130^(@)+sin10^(@)+sin140^(@)+sin20^(@)`
`" "=2sin70^(@)cos60^(@)+2sin80^(@)*cos60^(@)" "[becausesinx+siny=2sin""(x+y)/(2)*cos""(x-y)/(2)]`
`" "=2*(1)/(2)sin70^(@)+2*(1)/(2)sin80^(@)" "[becausecos60^(@)=(1)/(2)]`
`" "=sin70^(@)+sin80^(@)=sin""(7pi)/(18)+sin""(4pi)/(9)`
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  14. The value of sin(pi/18)+sin(pi/9)+sin((2pi)/9)+sin((5pi)/18) is

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